Motion Blur problems with wheels and Rigacar
The issue appears to be with the way that I created my instances. The origins of the instances of the wheels are at the center of the instances making them move smoothly in the viewport. However, the source of the instances has the origin of the tire set not at the center of the wheel.
To fix the problem: I applied all the modifiers on the tire tread and centered the tire's origin.
I also had to rebuild parts of the scene and the following paths in order to implement the new instances.